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Linear graph transformations on spaces of analytic functions

Aleman, Alexandru LU ; Perfekt, Karl-Mikael ; Richter, Stefan and Sundberg, Carl (2015) In Journal of Functional Analysis 268(9). p.2707-2734
Abstract
Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L-0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any... (More)
Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L-0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for M. (C) 2015 Elsevier Inc. All rights reserved. (Less)
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Transitive algebras, Invariant subspaces, Bergman space
in
Journal of Functional Analysis
volume
268
issue
9
pages
2707 - 2734
publisher
Elsevier
external identifiers
  • wos:000352465500008
  • scopus:84932196279
ISSN
0022-1236
DOI
10.1016/j.jfa.2015.01.012
language
English
LU publication?
yes
id
fc0db482-2b76-46a7-92e9-0d4301610f7d (old id 5402819)
date added to LUP
2016-04-01 13:34:09
date last changed
2022-01-27 19:53:03
@article{fc0db482-2b76-46a7-92e9-0d4301610f7d,
  abstract     = {{Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L-0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for M. (C) 2015 Elsevier Inc. All rights reserved.}},
  author       = {{Aleman, Alexandru and Perfekt, Karl-Mikael and Richter, Stefan and Sundberg, Carl}},
  issn         = {{0022-1236}},
  keywords     = {{Transitive algebras; Invariant subspaces; Bergman space}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{2707--2734}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Functional Analysis}},
  title        = {{Linear graph transformations on spaces of analytic functions}},
  url          = {{http://dx.doi.org/10.1016/j.jfa.2015.01.012}},
  doi          = {{10.1016/j.jfa.2015.01.012}},
  volume       = {{268}},
  year         = {{2015}},
}